Abstract:
The external feedback control problem in the Voigt model of the motion of a viscoelastic fluid is investigated. To this end, we prove the existence of weak solutions of the initial-boundary problem with the multi-valued right-hand side in the model considered and show the existence of a solution minimizing a given bounded lower semicontinuous functional.
Citation:
V. G. Zvyagin, M. Yu. Kuz'min, “On some optimal control problem in the Voigt model of the motion of a viscoelastic fluid”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, CMFD, 16, PFUR, M., 2006, 38–46; Journal of Mathematical Sciences, 149:5 (2008), 1618–1627
\Bibitem{ZvyKuz06}
\by V.~G.~Zvyagin, M.~Yu.~Kuz'min
\paper On some optimal control problem in the Voigt model of the motion of a~viscoelastic fluid
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~2
\serial CMFD
\yr 2006
\vol 16
\pages 38--46
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd47}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336444}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 5
\pages 1618--1627
\crossref{https://doi.org/10.1007/s10958-008-0085-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650678843}
Linking options:
https://www.mathnet.ru/eng/cmfd47
https://www.mathnet.ru/eng/cmfd/v16/p38
This publication is cited in the following 7 articles:
André Eikmeier, “Existence of strong solutions for the Oldroyd model with multivalued right-hand side”, Nonlinear Analysis, 225 (2022), 113127
V. G. Zvyagin, A. V. Zvyagin, M. V. Turbin, “Optimal Feedback Control Problem for the Bingham Model with Periodical Boundary Conditions on Spatial Variables”, J Math Sci, 244:6 (2020), 959
V. G. Zvyagin, A. V. Zvyagin, M. V. Turbin, “Optimalnoe upravlenie s obratnoi svyazyu dlya modeli Bingama s periodicheskimi usloviyami po prostranstvennym peremennym”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 47, K 85-letiyu Vsevoloda Alekseevicha SOLONNIKOVA, Zap. nauchn. sem. POMI, 477, POMI, SPb., 2018, 54–86
V. G. Zvyagin, “Topological approximation approach to study of mathematical problems of hydrodynamics”, Journal of Mathematical Sciences, 201:6 (2014), 830–858
Zvyagin V.G., Turbin M.V., “Optimal feedback control in the mathematical model of low concentrated aqueous polymer solutions”, J. Optim. Theory Appl., 148:1 (2011), 146–163
E. S. Baranovskii, “Optimal problems for parabolic-type systems with aspheric sets of admissible controls”, Russian Math. (Iz. VUZ), 53:12 (2009), 63–67
V. G. Zvyagin, M. V. Turbin, “The study of initial-boundary value problems for mathematical models of the motion of Kelvin–Voigt fluids”, Journal of Mathematical Sciences, 168:2 (2010), 157–308
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